We present a microscopic model for the anisotropic exchange interactions in Sr_2IrO_4. A direct construction of Wannier functions from first-principles calculations proves the j_<eff>=1/2 character of the spin-orbit integrated states at the Fermi level. An effective j_<eff>-spin Hamiltonian explains the observed weak ferromagnetism and anisotropy of antiferromagnetically ordered magnetic state, which arise naturally from the j_<eff>=1/2 state with a rotation of IrO_6 octahedra. It is suggested that Sr_2IrO_4 is a unique class of materials with effective exchange interactions in the spin-orbital Hilbert space.